2023 Yan Hus Tian @ York University. All Rights Reserved The law of total probability: Let A₁, A2,... A be mutually exclusive and exhaustive events, then for any other event B. P(B)=P(BA)*P(A) = P(B|A₁)*P(A₁)+P(B\A₂)*P(A₂)+...+P(B\A)*P(A). Example 2.10 Example 2.30 P81 One people has three email accounts: A, B, C. 1. Find probability that a randomly selected email is from A and is a spam. 2. Find probability that a randomly selected email is spam? A B C 70% 20% 10% 1% 2% 5% probability of receiving email probability of spam received email to 1. P(Spam | A) = December 10, 2023 P (Spam Received email) P (Received from A) 3 P(Span1B) = 1³ (SpainB! PCB) 10.02 0.2 0.01 0.10 = = 0.0143.
2023 Yan Hus Tian @ York University. All Rights Reserved The law of total probability: Let A₁, A2,... A be mutually exclusive and exhaustive events, then for any other event B. P(B)=P(BA)*P(A) = P(B|A₁)*P(A₁)+P(B\A₂)*P(A₂)+...+P(B\A)*P(A). Example 2.10 Example 2.30 P81 One people has three email accounts: A, B, C. 1. Find probability that a randomly selected email is from A and is a spam. 2. Find probability that a randomly selected email is spam? A B C 70% 20% 10% 1% 2% 5% probability of receiving email probability of spam received email to 1. P(Spam | A) = December 10, 2023 P (Spam Received email) P (Received from A) 3 P(Span1B) = 1³ (SpainB! PCB) 10.02 0.2 0.01 0.10 = = 0.0143.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Can you explain each part
Transcribed Image Text:2023 Yan Hun Tian @ York University. All Rights Reserved
The law of total probability: Let A₁, A2... A be mutually exclusive and
exhaustive events, then for any other event B.
P(B)=P(BA₁)*P(A₂) = P(B|A₁)*P(A₁)+P(B\A₂)*P(A₂)+...+P(B\A)*P(AR).
Example 2.10 Example 2.30 P81 One people has three email accounts: A, B, C.
1. Find probability that a randomly selected email is from A and is a spam.
2. Find probability that a randomly selected email is spam?
A B C
70% 20% 10%
P (Spa 1B) = 1³ (SpánB!
PCB)
Coyon
0.2
1% 2% 5%
probability of receiving email
probability of spam
bus 971
1. P(Spam | A) =
December 10, 2023
received email to
P (Spam Received email)
P (Received from A)
0.01
0.10
= 0.0143.
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